In addition to the advice above, I'd suggest you pay attention to the types of 2-minute requests you're getting. Is there a pattern? Are they all around similar issues, or from a similar person? Is there any way you can stem the flow?
For example, I was once getting a lot of questions on various aspects of a project I was working on. They were all pretty easy to deal with, but they kept coming in day after day from various people. Many of them were really the same question from different people. So I set up an intranet page that explained that part of the project in sufficient detail to answer the typical questions I was getting. I just copy-n-pasted questions and answers from my Sent Items folder to get the page set up, so it didn't take long at all.
From then on, whenever somebody asked a question I sent them back the URL. If it was a question that the page didn't answer properly, I added the answer before sending them the URL. Pretty soon, most people would check the page first before emailing me, and the incoming interruptions almost ceased (on that topic, at least!).
Look for opportunities to do this in your situation.